Rotationally inelastic collisions between a diatomic molecule in a2Π electronic state and a structureless target

Abstract

We present the full close‐coupling formulation of the collision between a diatomic molecule in a ²Π state in the Hund’s case (a) limit and a structureless target. Due to the possibility of transitions between spin‐orbit and/or Λ‐doubling states the scattering displays an additional degree of complexity not seen in rotationally inelastic collisions of ¹Σ⁺ molecules. The well‐known coupled states and infinite‐order‐sudden (IOS) approximation techniques can be applied in a straightforward manner. The factorization and scaling relations between the various cross sections, which are valid in the energy sudden limit, are explored. For transitions within either spin‐orbit manifold (Ω = 1/2, Ω = 3/2), these scaling relations allow both matrices of cross sections, for parity conserving the parity violating transitions, to be expressed in terms of the cross sections for parity conserving transitions out of the Ω = 1/2, J = 1/2 level. Under conditions in which either a Born or sudden formulation of the collision dynamics is appropriate, we show that at large values of the total angular momentum, transitions which conserve the parity index of the molecular wave functions will be strongly favored, a propensity rule which has been seen in previous experimental studies of rotational relaxation in ²Π molecules. A scaling relation is also derived for the cross sections for transitions between the two spin‐orbit manifolds. For these processes, however, the propensity toward conservation of the parity index only occurs in the case of transitions which are elastic in the total angular momentum. The IOS formulation of the collision dynamics is then extended to a Hund’s case (b) representation of the molecular wave function. Although a complete factorization is no longer possible, one can still show that at large J there will exist a strong propensity toward conservation of the alignment between S (the spin‐angular momentum of the molecule) and N (the vector sum of the nuclear rotational angular momentum R and the z‐component Λ of the electronic orbital angular momentum). In the case (b) limit a propensity toward conservation of the parity index will still exist, but less strongly than in the case (a) limit.